The present invention relates to an induction motor control apparatus and, more particularly, to an induction motor control apparatus wherein the smoothness of rotation of an induction motor at a low speed can be greatly improved.
Conventional induction motors have served as constant-speed motors using a power source having a predetermined frequency and have been used in a variety of applications in favor of rigidness and low cost.
Along with the recent development of electronic devices, microcomputers, and software, a power source having a wide variable frequency range on the basis of vector control (to be referred to as a "driver" hereinafter) can be provided as a power source for driving induction motors. Therefore, induction motors have been popular as servo motors. The above driver is vector-controlled on the basis of the following principle.
The fundamental equations used in vector control are given by a torque current i.sub.1q, an excitation current or a magnetic flux component current i.sub.1d for generating a secondary flux .PHI..sub.2, and a slip speed .omega..sub.s as follows: EQU i.sub.1q =(L.sub.2 /M)(T/.PHI..sub.2) (1) EQU i.sub.1d ={.PHI..sub.2 +(L.sub.2 /R.sub.2)(d.PHI..sub.2 /dt)}/M (2) ##EQU1## where L.sub.2 is the secondary inductance, M is the mutual inductance, T is the torque, .PHI..sub.2 is the secondary magnetic flux, and R.sub.2 is the secondary resistance.
The torque T in equations (1) and (3) is an instruction value applied to the vector control apparatus for vector control. The secondary magnetic flux .PHI..sub.2 is a preset value determined in advance.
The torque T is derived from equations (1), (2), and (3) as follows: EQU T=(M.sup.2 /R.sub.2).omega..sub.s i.sub.1d.sup.2 =(M.sup.2 /L.sub.2)i.sub.1d i.sub.1q ( 4)
After the slip speed .omega..sub.s, the torque current i.sub.1q, and the excitation current i.sub.1d are thus determined, they are used to control a so-called inverter which supplies power to the induction motor in such a manner that the induction motor can be driven to provide desired characteristics.
FIG. 1 is a block diagram showing a conventional basic arrangement of a slip frequency vector control apparatus to realize the above-mentioned principle.
Referring to FIG. 1, reference numeral 1 denotes a speed control amplifier; 2, a divider; 3, a constant multiplier; 4, a vector analyzer; 5, a multiplier; 6, a converter; 7, a current control amplifier; 8, a power converter; 9, an induction motor; 11, a speed sensor; 12, a differentiator; 13, 14, 15, and 16, constant multipliers; 17, a divider; 18, a vector oscillator; and 19 and 20, adders.
In operation, an output from the speed control amplifier 1 is provided as a torque instruction T.sub.M.sup.*. The torque instruction T.sub.M.sup.* is divided by the secondary magnetic flux instruction .PHI..sub.2.sup.* in the divider 2 to obtain a secondary q-axis current instruction -i.sub.2q.sup.*. The constant multiplier 3 multiples the instruction -i.sub.2q.sup.* with constant L.sub.2 /M, thereby deriving a torque component current instruction i.sub.1q.sup.*.
A magnetic flux component current instruction i.sub.1d.sup.* is derived from the secondary magnetic flux instruction .PHI..sub.2.sup.* as follows. In order to compensate for primary delay of the secondary flux .PHI..sub.2 from a magnetic flux component current i.sub.1d, a current for generating the secondary flux obtained by multiplying the secondary flux instruction .PHI..sub.2.sup.* with 1/M in the multiplier 15 is added to a current for forcing the secondary flux proportional to a rate of change in time of the secondary flux instruction .PHI..sub.2.sup.* through the differentiator 12 and the multipliers 13 and 14 to obtain the magnetic flux component current instruction i.sub.1d.sup.*.
A slip frequency instruction .omega..sub.s.sup.* is calculated using the secondary flux instruction .PHI..sub.2.sup.* and the secondary q-axis current instruction -i.sub.2q.sup.*. A real speed .omega..sub.r from the speed sensor 11 is added to the slip frequency instruction .omega..sub.s.sup.* by the adder 20 to obtain a secondary flux speed .omega..sub.0.sup.* which is then input to the vector oscillator 18. Therefore, a unit vector .sub.e j.theta..sub.0.sup.* representing a predictive position .theta..sub.0.sup.* of the secondary flux is generated by the vector oscillator 18.
A primary current vector i.sub.1.sup.* (.theta..sub.0.sup.*) determined by the torque component current and the magnetic flux component instruction value and plotted on the secondary magnetic flux coordinate system is multiplied with the unit vector .sub.e j.theta..sub.0.sup.* by the multiplier 5 and is thus converted into a primary current vector i.sub.1.sup.* on the fixed coordinates. The primary current vector i.sub.1.sup.* is 3-phase converted to obtain current instruction values i.sub.u.sup.*, i.sub.v.sup.*, and i.sub.w.sup.* of the respective phases, thereby causing a current control loop to control the current control amplifier 7 and the power converter 8.
Changes in the instantaneous induction motor torque can be controlled as a function of the instantaneous current.
However, in the "slip frequency vector control apparatus" shown in FIG. 1, the following problems are posed when the induction motor serves as a servo motor. Smooth rotation, i.e., a small rotational variation of the servo motor is required in a low speed range when high-precision control such as table feeding for finishing in a machine tool is to be performed. For this purpose, a rated torque must be generated during the operation of the induction motor. A torque T.sub.G during the operation of the induction motor must be substantially equal to a steady, constant (without irregularity) loading torque T.sub.L when the induction motor is operated generating the torque T.sub.L. In other words, if the relation T.sub.G =T.sub.L +.DELTA.T is established, the torque ripple .DELTA.T must be minimized. It should be noted that the cause of the torque ripple .DELTA.T is a magnetomotive force due to harmonic components with respect to space and time of a frequency f.sub.1 of the primary current supplied from the driver to the primary winding of the induction motor.
In a driver for generating electric energy having a simple 3.PHI. rectangular voltage waveform, electric energy includes harmonic components with respect to time of 6k.+-.1 times (k=1, 2, 3, . . . ) the primary frequency f.sub.1. Therefore, the torque ripple components of the frequency of 6kf.sub.1 are naturally generated in the force wave proportional to the torque T.sub.G of the induction motor.
Along with recent developments of electronic devices (e.g., LSIs and power-controlled semiconductor elements), sensors (e.g., current, speed, and position sensors), and software techniques for high-precision, high-speed data processing, a driver capable of supplying electric energy having almost a sinusoidal wave in a variable frequency range has been commercially available in recent years.
When a primary current having a substantially ideal sinusoidal wave is supplied to an induction motor and the induction motor is operated in a wide range of primary frequencies f.sub.1, frequencies of major components of the torque ripple are 2f.sub.1 and the like in a relatively high motor speed range. However, when the motor speed is reduced, the component 2f.sub.1 or the like is not so conspicuous. Instead, harmonic components 6kf.sub.1 typically appear.
FIG. 2 is a graph showing an induction motor torque spectrum measured by a torque spectrum sensor, and FIG. 3 shows a natural spectrum (multiples of 15 Hz and 50 Hz) of the torque spectrum sensor. In the torque spectrum of FIG. 2, hatched portions indicate influence of the torque spectrum sensor.
As is apparent from FIG. 2, torque ripples at frequencies of 2f.sub.1 and 6kf.sub.1 have large values. This phenomenon also occurs when the output is a sinusoidal wave in addition to the rectangular wave. No proper explanation is given for generation of torque ripples at frequencies of 6kf.sub.1 when the sinusoidal primary current is supplied to the induction motor. No effective countermeasures for this have been proposed.
However, the harmonic torque components .DELTA.T at the frequencies of 6kf.sub.1 at almost zero speed are decisive drawbacks for high-precision servo motors.